Instruction 13-6
One of the Most Common Questions of Prospective

Multiple Choice

Instruction 13-6
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y) .
To provide its customers with information on that matter,a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X₁) ,the amount of insulation in cm (X₂) ,the number of windows in the house (X₃) ,and the age of the furnace in years (X₄) .Given below are the Microsoft Excel outputs of two regression models.
$\begin{array}{lr}{\text { Model 1 }} \\\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\text { Adjusted R Square } & 0.7568 \\\text { Observations } & 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrrr}\hline & d f & & S S & M S & F & \text { Significance } F \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 \mathrm{E}-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {\text { P-value }} & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05 & 284.9327 & 557.9227 \\\mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$ $\begin{array}{l}\text { Model } 2\\\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\text { Adjusted R } & \\\text { Square } & 0.7506 \\\text { Observations } & 20 \\\hline\end{array}\end{array}$
ANOVA
$\begin{array}{lrrrrrr} & d f & &{\text { SS }} & M S & F & \text { Significance } F \\\hline \text { Regression } & & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\\text { Residual } & 17 & 46807.5222 & 2753.384 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 3.17 \mathrm{E}-09 & 396.5273 & 582.1180 \\\mathrm{X}_{1} \text { (Temperature) } & -5.1103 & 0.6951 & -7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\mathrm{X}_{2} \text { (Insulation) } & -14.7195 & 4.8864 & -3.0123 & 0.0078 & -25.0290 & -4.4099\end{array}$
-Referring to Instruction 13-6 and allowing for a 1% probability of committing a Type I error,what is the decision and conclusion for the test H₀: ?₁ = ?₂ = ?₃ = ?₄ = 0 vs.H₁: At least one ?_j ? 0,j = 1,2,... ,4 using Model 1?

A) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
B) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
C) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on average heating costs.
D) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.